Complete this table with the given function values.

[tex]\[
f\left(\frac{-1}{2}\right) = -2 \\
f(0) = \frac{3}{2} \\
f(1) = -1 \\
f(2) = 1 \\
f(4) = \frac{7}{2}
\][/tex]



Answer :

Certainly! Let's delve into solving the given mathematical expressions step by step.

We are given a function [tex]\( f \)[/tex] with specific values at certain points. The values are:

1. [tex]\( f\left( \frac{-1}{2} \right) = -2 \)[/tex]
2. [tex]\( f(0) = \frac{3}{2} \)[/tex]
3. [tex]\( f(1) = -1 \)[/tex]
4. [tex]\( f(2) = 1 \)[/tex]
5. [tex]\( f(4) = \frac{7}{2} \)[/tex]

Let's go through each one:

1. At [tex]\( x = \frac{-1}{2} \)[/tex]:
[tex]\[ f\left( \frac{-1}{2} \right) = -2 \][/tex]

2. At [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = \frac{3}{2} \][/tex]

3. At [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = -1 \][/tex]

4. At [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 1 \][/tex]

5. At [tex]\( x = 4 \)[/tex]:
[tex]\[ f(4) = \frac{7}{2} \][/tex]

To summarize, the values of [tex]\( f(x) \)[/tex] at the specified points are:

- [tex]\( f\left( \frac{-1}{2} \right) = -2 \)[/tex]
- [tex]\( f(0) = \frac{3}{2} \)[/tex]
- [tex]\( f(1) = -1 \)[/tex]
- [tex]\( f(2) = 1 \)[/tex]
- [tex]\( f(4) = \frac{7}{2} \)[/tex]

Thus, the function [tex]\( f \)[/tex] evaluated at the given points results in:
[tex]\[ \left( -\frac{1}{2}, -2 \right), (0, \frac{3}{2}), (1, -1), (2, 1), (4, \frac{7}{2}) \][/tex]

These are the coordinates of the points that the function [tex]\( f \)[/tex] takes.